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<div class="title">polar_decomposition_3x3_matrix.h</div>  </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">// MIT License</span></div><div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="comment">// </span></div><div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment">// Copyright (c) 2017 Martin Bisson</span></div><div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment">// </span></div><div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment">// Permission is hereby granted, free of charge, to any person obtaining a copy</span></div><div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment">// of this software and associated documentation files (the &quot;Software&quot;), to deal</span></div><div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment">// in the Software without restriction, including without limitation the rights</span></div><div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment">// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell</span></div><div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="comment">// copies of the Software, and to permit persons to whom the Software is</span></div><div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="comment">// furnished to do so, subject to the following conditions:</span></div><div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="comment">// </span></div><div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;<span class="comment">// The above copyright notice and this permission notice shall be included in all</span></div><div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="comment">// copies or substantial portions of the Software.</span></div><div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<span class="comment">// </span></div><div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="comment">// THE SOFTWARE IS PROVIDED &quot;AS IS&quot;, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR</span></div><div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="comment">// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,</span></div><div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;<span class="comment">// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE</span></div><div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;<span class="comment">// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER</span></div><div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;<span class="comment">// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,</span></div><div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;<span class="comment">// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE</span></div><div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;<span class="comment">// SOFTWARE.</span></div><div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;<span class="preprocessor">#ifndef __POLAR_DECOMPOSITION_3X3_MATRIX_H__</span></div><div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;<span class="preprocessor">#define __POLAR_DECOMPOSITION_3X3_MATRIX_H__</span></div><div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;</div><div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;</div><div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;</div><div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;</div><div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;<span class="preprocessor">#include &lt;cassert&gt;</span></div><div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;<span class="preprocessor">#include &lt;cmath&gt;</span></div><div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;<span class="preprocessor">#include &lt;limits&gt;</span></div><div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;</div><div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;</div><div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespacepolar.html">polar</a></div><div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;{</div><div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;</div><div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;</div><div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;    <span class="keyword">namespace </span>detail</div><div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;    {</div><div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;</div><div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;</div><div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;        <span class="comment">// Helper methods for standard mathematical function calls.</span></div><div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;        <span class="keyword">template</span> &lt;<span class="keyword">typename</span> TReal&gt;</div><div class="line"><a name="l00043"></a><span class="lineno"><a class="line" href="structpolar_1_1detail_1_1math__utils.html">   43</a></span>&#160;        <span class="keyword">struct </span><a class="code" href="structpolar_1_1detail_1_1math__utils.html">math_utils</a></div><div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;        {</div><div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;            <span class="keyword">static</span> <span class="keyword">inline</span> TReal sqrt(<span class="keyword">const</span> TReal x);</div><div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;            <span class="keyword">static</span> <span class="keyword">inline</span> TReal fabs(<span class="keyword">const</span> TReal x);</div><div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;            <span class="keyword">static</span> <span class="keyword">inline</span> TReal clamp(<span class="keyword">const</span> TReal x, <span class="keyword">const</span> TReal a, <span class="keyword">const</span> TReal b);</div><div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;            <span class="keyword">static</span> <span class="keyword">inline</span> TReal cos(<span class="keyword">const</span> TReal x);</div><div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;            <span class="keyword">static</span> <span class="keyword">inline</span> TReal acos(<span class="keyword">const</span> TReal x);</div><div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;            <span class="keyword">static</span> <span class="keyword">inline</span> TReal ceil(<span class="keyword">const</span> TReal x);</div><div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;            <span class="keyword">static</span> <span class="keyword">inline</span> TReal log10(<span class="keyword">const</span> TReal x);</div><div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;        };</div><div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;</div><div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;        <span class="keyword">template</span> &lt;&gt;</div><div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;        <span class="keyword">inline</span> <span class="keywordtype">float</span> <a class="code" href="structpolar_1_1detail_1_1math__utils.html">math_utils&lt;float&gt;::sqrt</a>(<span class="keyword">const</span> <span class="keywordtype">float</span> x)</div><div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;        {</div><div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;            return ::sqrtf(x);</div><div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;        }</div><div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;        <span class="keyword">template</span> &lt;&gt;</div><div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;        <span class="keyword">inline</span> <span class="keywordtype">double</span> math_utils&lt;double&gt;::sqrt(<span class="keyword">const</span> <span class="keywordtype">double</span> x)</div><div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;        {</div><div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;            return ::sqrt(x);</div><div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;        }</div><div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;</div><div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;        <span class="keyword">template</span> &lt;&gt;</div><div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;        <span class="keyword">inline</span> <span class="keywordtype">float</span> math_utils&lt;float&gt;::fabs(<span class="keyword">const</span> <span class="keywordtype">float</span> x)</div><div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;        {</div><div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;            return ::fabs(x);</div><div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;        }</div><div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;        <span class="keyword">template</span> &lt;&gt;</div><div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;        <span class="keyword">inline</span> <span class="keywordtype">double</span> math_utils&lt;double&gt;::fabs(<span class="keyword">const</span> <span class="keywordtype">double</span> x)</div><div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;        {</div><div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;            return ::fabs(x);</div><div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;        }</div><div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;</div><div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;        <span class="keyword">template</span> &lt;<span class="keyword">typename</span> TReal&gt;</div><div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;        <span class="keyword">inline</span> TReal math_utils&lt;TReal&gt;::clamp(<span class="keyword">const</span> TReal x, <span class="keyword">const</span> TReal a, <span class="keyword">const</span> TReal b)</div><div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;        {</div><div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;            assert(a &lt;= b);</div><div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;            <span class="keywordflow">if</span> (x &lt; a)</div><div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;                <span class="keywordflow">return</span> a;</div><div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;            <span class="keywordflow">else</span> <span class="keywordflow">if</span> (x &gt; b)</div><div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;                <span class="keywordflow">return</span> b;</div><div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;            <span class="keywordflow">else</span></div><div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;                <span class="keywordflow">return</span> x;</div><div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;        }</div><div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;</div><div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;        <span class="keyword">template</span> &lt;&gt;</div><div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;        <span class="keyword">inline</span> <span class="keywordtype">float</span> math_utils&lt;float&gt;::cos(<span class="keyword">const</span> <span class="keywordtype">float</span> x)</div><div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;        {</div><div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;            return ::cosf(x);</div><div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;        }</div><div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;        <span class="keyword">template</span> &lt;&gt;</div><div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;        <span class="keyword">inline</span> <span class="keywordtype">double</span> math_utils&lt;double&gt;::cos(<span class="keyword">const</span> <span class="keywordtype">double</span> x)</div><div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;        {</div><div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;            return ::cos(x);</div><div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;        }</div><div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;</div><div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;        <span class="keyword">template</span> &lt;&gt;</div><div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;        <span class="keyword">inline</span> <span class="keywordtype">float</span> math_utils&lt;float&gt;::acos(<span class="keyword">const</span> <span class="keywordtype">float</span> x)</div><div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;        {</div><div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;            return ::acosf(x);</div><div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;        }</div><div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;        <span class="keyword">template</span> &lt;&gt;</div><div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;        <span class="keyword">inline</span> <span class="keywordtype">double</span> math_utils&lt;double&gt;::acos(<span class="keyword">const</span> <span class="keywordtype">double</span> x)</div><div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;        {</div><div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;            return ::acos(x);</div><div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;        }</div><div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;</div><div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;        <span class="keyword">template</span> &lt;&gt;</div><div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;        <span class="keyword">inline</span> <span class="keywordtype">float</span> math_utils&lt;float&gt;::ceil(<span class="keyword">const</span> <span class="keywordtype">float</span> x)</div><div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;        {</div><div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;            return ::ceilf(x);</div><div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;        }</div><div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;        <span class="keyword">template</span> &lt;&gt;</div><div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;        <span class="keyword">inline</span> <span class="keywordtype">double</span> math_utils&lt;double&gt;::ceil(<span class="keyword">const</span> <span class="keywordtype">double</span> x)</div><div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;        {</div><div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;            return ::ceil(x);</div><div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;        }</div><div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;</div><div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;        <span class="keyword">template</span> &lt;&gt;</div><div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;        <span class="keyword">inline</span> <span class="keywordtype">float</span> math_utils&lt;float&gt;::log10(<span class="keyword">const</span> <span class="keywordtype">float</span> x)</div><div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;        {</div><div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;            return ::log10f(x);</div><div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;        }</div><div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;        <span class="keyword">template</span> &lt;&gt;</div><div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;        <span class="keyword">inline</span> <span class="keywordtype">double</span> math_utils&lt;double&gt;::log10(<span class="keyword">const</span> <span class="keywordtype">double</span> x)</div><div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;        {</div><div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;            return ::log10(x);</div><div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;        }</div><div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;</div><div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;</div><div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;    }; <span class="comment">// End of namespace detail.</span></div><div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;</div><div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;</div><div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;</div><div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;</div><div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;    <span class="comment">// Implementation of the basic matrix type used in the algorithm.</span></div><div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;    <span class="keyword">namespace </span>detail</div><div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;    {</div><div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;</div><div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;</div><div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;        <span class="comment">// Definition of the column-major matrix type.</span></div><div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;        <span class="keyword">template</span> &lt;<span class="keyword">typename</span> TReal, <span class="keywordtype">int</span> NbColumns, <span class="keywordtype">int</span> NbRows&gt;</div><div class="line"><a name="l00145"></a><span class="lineno"><a class="line" href="classpolar_1_1detail_1_1matrix.html">  145</a></span>&#160;        <span class="keyword">class </span><a class="code" href="classpolar_1_1detail_1_1matrix.html">matrix</a></div><div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;        {</div><div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;        <span class="keyword">public</span>:</div><div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;            <span class="keyword">inline</span> TReal  operator()(<span class="keywordtype">int</span> columnIndex, <span class="keywordtype">int</span> rowIndex) <span class="keyword">const</span>;</div><div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;            <span class="keyword">inline</span> TReal&amp; operator()(<span class="keywordtype">int</span> columnIndex, <span class="keywordtype">int</span> rowIndex);</div><div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;            <span class="keyword">inline</span> TReal  operator()(<span class="keywordtype">int</span> index) <span class="keyword">const</span>;</div><div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;            <span class="keyword">inline</span> TReal&amp; operator()(<span class="keywordtype">int</span> index);</div><div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;</div><div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;        <span class="keyword">private</span>:</div><div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;            TReal data[NbColumns * NbRows];</div><div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;        };</div><div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;</div><div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;</div><div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;        <span class="comment">// We rely on the compiler to be efficient in inlining the calls to this</span></div><div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;        <span class="comment">// method, and especially optimize the double-indices access and convert them</span></div><div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;        <span class="comment">// to single access ones.</span></div><div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;        <span class="keyword">template</span> &lt;<span class="keyword">typename</span> TReal, <span class="keywordtype">int</span> NbRows, <span class="keywordtype">int</span> NbColumns&gt;</div><div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;        <span class="keyword">inline</span> TReal <a class="code" href="classpolar_1_1detail_1_1matrix.html">matrix&lt;TReal, NbRows, NbColumns&gt;::operator()</a>(<span class="keywordtype">int</span> columnIndex, <span class="keywordtype">int</span> rowIndex)<span class="keyword"> const</span></div><div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;<span class="keyword">        </span>{</div><div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;            assert(0 &lt;= rowIndex);</div><div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;            assert(rowIndex &lt; NbRows);</div><div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;            assert(0 &lt;= columnIndex);</div><div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;            assert(columnIndex &lt; NbColumns);</div><div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;            <span class="keywordflow">return</span> data[columnIndex * NbRows + rowIndex];</div><div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;        }</div><div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;</div><div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;        <span class="keyword">template</span> &lt;<span class="keyword">typename</span> TReal, <span class="keywordtype">int</span> NbRows, <span class="keywordtype">int</span> NbColumns&gt;</div><div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;        <span class="keyword">inline</span> TReal&amp; matrix&lt;TReal, NbRows, NbColumns&gt;::operator()(<span class="keywordtype">int</span> columnIndex, <span class="keywordtype">int</span> rowIndex)</div><div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;        {</div><div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;            assert(0 &lt;= rowIndex);</div><div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;            assert(rowIndex &lt; NbRows);</div><div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;            assert(0 &lt;= columnIndex);</div><div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;            assert(columnIndex &lt; NbColumns);</div><div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;            <span class="keywordflow">return</span> data[columnIndex * NbRows + rowIndex];</div><div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;        }</div><div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;</div><div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;        <span class="keyword">template</span> &lt;<span class="keyword">typename</span> TReal, <span class="keywordtype">int</span> NbRows, <span class="keywordtype">int</span> NbColumns&gt;</div><div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;        <span class="keyword">inline</span> TReal matrix&lt;TReal, NbRows, NbColumns&gt;::operator()(<span class="keywordtype">int</span> index)<span class="keyword"> const</span></div><div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;<span class="keyword">        </span>{</div><div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;            assert(0 &lt;= index);</div><div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;            assert(index &lt; NbRows * NbColumns);</div><div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;            <span class="keywordflow">return</span> data[index];</div><div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;        }</div><div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;</div><div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;        <span class="keyword">template</span> &lt;<span class="keyword">typename</span> TReal, <span class="keywordtype">int</span> NbRows, <span class="keywordtype">int</span> NbColumns&gt;</div><div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;        <span class="keyword">inline</span> TReal&amp; matrix&lt;TReal, NbRows, NbColumns&gt;::operator()(<span class="keywordtype">int</span> index)</div><div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;        {</div><div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;            assert(0 &lt;= index);</div><div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;            assert(index &lt; NbRows * NbColumns);</div><div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;            <span class="keywordflow">return</span> data[index];</div><div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;        }</div><div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;</div><div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;</div><div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;        <span class="comment">// Definition of the vector type.</span></div><div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;        <span class="keyword">template</span> &lt;<span class="keyword">typename</span> TReal, <span class="keywordtype">int</span> NbElements&gt;</div><div class="line"><a name="l00200"></a><span class="lineno"><a class="line" href="classpolar_1_1detail_1_1vector.html">  200</a></span>&#160;        <span class="keyword">class </span><a class="code" href="classpolar_1_1detail_1_1vector.html">vector</a></div><div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;        {</div><div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;        <span class="keyword">public</span>:</div><div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;            <span class="keyword">inline</span> TReal  operator()(<span class="keywordtype">int</span> index) <span class="keyword">const</span>;</div><div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;            <span class="keyword">inline</span> TReal&amp; operator()(<span class="keywordtype">int</span> index);</div><div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;</div><div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;        <span class="keyword">private</span>:</div><div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;            TReal data[NbElements];</div><div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;        };</div><div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;</div><div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;</div><div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;        <span class="keyword">template</span> &lt;<span class="keyword">typename</span> TReal, <span class="keywordtype">int</span> NbElements&gt;</div><div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;        <span class="keyword">inline</span> TReal <a class="code" href="classpolar_1_1detail_1_1vector.html">vector&lt;TReal, NbElements&gt;::operator()</a>(<span class="keywordtype">int</span> index)<span class="keyword"> const</span></div><div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;<span class="keyword">        </span>{</div><div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;            assert(0 &lt;= index);</div><div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;            assert(index &lt; NbElements);</div><div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;            <span class="keywordflow">return</span> data[index];</div><div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;        }</div><div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;</div><div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;        <span class="keyword">template</span> &lt;<span class="keyword">typename</span> TReal, <span class="keywordtype">int</span> NbElements&gt;</div><div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;        <span class="keyword">inline</span> TReal&amp; vector&lt;TReal, NbElements&gt;::operator()(<span class="keywordtype">int</span> index)</div><div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;        {</div><div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;            assert(0 &lt;= index);</div><div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;            assert(index &lt; NbElements);</div><div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;            <span class="keywordflow">return</span> data[index];</div><div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;        }</div><div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;</div><div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;</div><div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160;        <span class="comment">//</span></div><div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;        <span class="comment">// The following re-implements matrix operations that are very common in</span></div><div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;        <span class="comment">// most linear algebra packages such as GLM or Eigen.  However, by design</span></div><div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160;        <span class="comment">// this library does not want to depend on such packages, so the simple</span></div><div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160;        <span class="comment">// matrix operations are re-implemented here.</span></div><div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160;        <span class="comment">//</span></div><div class="line"><a name="l00234"></a><span class="lineno">  234</span>&#160;        <span class="comment">// Most methods are not implemented in the most generic way; they are</span></div><div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160;        <span class="comment">// specialized for the ways they are used in this algorithm specific</span></div><div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160;        <span class="comment">// implementation.</span></div><div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160;        <span class="comment">//</span></div><div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160;        <span class="comment">// They definitely could be implemented in a &quot;cleaner&quot;, shorter way</span></div><div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;        <span class="comment">// using the proper libraries.</span></div><div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160;        <span class="comment">//</span></div><div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;</div><div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;        <span class="keyword">template</span> &lt;<span class="keyword">typename</span> TReal&gt;</div><div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;        <span class="keyword">inline</span> <span class="keywordtype">void</span> normalize(matrix&lt;TReal, 3, 3&gt;&amp; m)</div><div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160;        {</div><div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160;            TReal length = m(0) * m(0);</div><div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160;            length += m(1) * m(1);</div><div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;            length += m(2) * m(2);</div><div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160;            length += m(3) * m(3);</div><div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;            length += m(4) * m(4);</div><div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;            length += m(5) * m(5);</div><div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;            length += m(6) * m(6);</div><div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;            length += m(7) * m(7);</div><div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;            length += m(8) * m(8);</div><div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;</div><div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;            <span class="comment">// Add small numerical value to make sure we are ok with 0-length.</span></div><div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160;            <span class="keyword">const</span> TReal factor = 1 / (math_utils&lt;TReal&gt;::sqrt(length) + (std::numeric_limits&lt;TReal&gt;::min)());</div><div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160;</div><div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160;            m(0) *= factor;</div><div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160;            m(1) *= factor;</div><div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160;            m(2) *= factor;</div><div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;            m(3) *= factor;</div><div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160;            m(4) *= factor;</div><div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;            m(5) *= factor;</div><div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;            m(6) *= factor;</div><div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160;            m(7) *= factor;</div><div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;            m(8) *= factor;</div><div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;        }</div><div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160;</div><div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160;        <span class="keyword">template</span> &lt;<span class="keyword">typename</span> TReal&gt;</div><div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160;        <span class="keyword">inline</span> <span class="keywordtype">void</span> normalize(vector&lt;TReal, 4&gt;&amp; m)</div><div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160;        {</div><div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160;            TReal length = m(0) * m(0);</div><div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160;            length += m(1) * m(1);</div><div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160;            length += m(2) * m(2);</div><div class="line"><a name="l00275"></a><span class="lineno">  275</span>&#160;            length += m(3) * m(3);</div><div class="line"><a name="l00276"></a><span class="lineno">  276</span>&#160;</div><div class="line"><a name="l00277"></a><span class="lineno">  277</span>&#160;            <span class="comment">// Add small numerical value to make sure we are ok with 0-length.</span></div><div class="line"><a name="l00278"></a><span class="lineno">  278</span>&#160;            <span class="keyword">const</span> TReal factor = 1 / (math_utils&lt;TReal&gt;::sqrt(length) + (std::numeric_limits&lt;TReal&gt;::min)());</div><div class="line"><a name="l00279"></a><span class="lineno">  279</span>&#160;</div><div class="line"><a name="l00280"></a><span class="lineno">  280</span>&#160;            m(0) *= factor;</div><div class="line"><a name="l00281"></a><span class="lineno">  281</span>&#160;            m(1) *= factor;</div><div class="line"><a name="l00282"></a><span class="lineno">  282</span>&#160;            m(2) *= factor;</div><div class="line"><a name="l00283"></a><span class="lineno">  283</span>&#160;            m(3) *= factor;</div><div class="line"><a name="l00284"></a><span class="lineno">  284</span>&#160;        }</div><div class="line"><a name="l00285"></a><span class="lineno">  285</span>&#160;</div><div class="line"><a name="l00286"></a><span class="lineno">  286</span>&#160;</div><div class="line"><a name="l00287"></a><span class="lineno">  287</span>&#160;        <span class="keyword">template</span> &lt;<span class="keyword">typename</span> TReal&gt;</div><div class="line"><a name="l00288"></a><span class="lineno">  288</span>&#160;        <span class="keyword">inline</span> <span class="keywordtype">void</span> transpose_multiply(</div><div class="line"><a name="l00289"></a><span class="lineno">  289</span>&#160;            matrix&lt;TReal, 3, 3&gt;&amp; result,</div><div class="line"><a name="l00290"></a><span class="lineno">  290</span>&#160;            <span class="keyword">const</span> matrix&lt;TReal, 3, 3&gt;&amp; a,</div><div class="line"><a name="l00291"></a><span class="lineno">  291</span>&#160;            <span class="keyword">const</span> matrix&lt;TReal, 3, 3&gt;&amp; b</div><div class="line"><a name="l00292"></a><span class="lineno">  292</span>&#160;            )</div><div class="line"><a name="l00293"></a><span class="lineno">  293</span>&#160;        {</div><div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160;            <span class="comment">// Perform transposition at the same time as the multiplication.</span></div><div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160;            result(0,0) = a(0,0) * b(0,0) + a(0,1) * b(0,1) + a(0,2) * b(0,2);</div><div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160;            result(0,1) = a(1,0) * b(0,0) + a(1,1) * b(0,1) + a(1,2) * b(0,2);</div><div class="line"><a name="l00297"></a><span class="lineno">  297</span>&#160;            result(0,2) = a(2,0) * b(0,0) + a(2,1) * b(0,1) + a(2,2) * b(0,2);</div><div class="line"><a name="l00298"></a><span class="lineno">  298</span>&#160;            result(1,0) = a(0,0) * b(1,0) + a(0,1) * b(1,1) + a(0,2) * b(1,2);</div><div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160;            result(1,1) = a(1,0) * b(1,0) + a(1,1) * b(1,1) + a(1,2) * b(1,2);</div><div class="line"><a name="l00300"></a><span class="lineno">  300</span>&#160;            result(1,2) = a(2,0) * b(1,0) + a(2,1) * b(1,1) + a(2,2) * b(1,2);</div><div class="line"><a name="l00301"></a><span class="lineno">  301</span>&#160;            result(2,0) = a(0,0) * b(2,0) + a(0,1) * b(2,1) + a(0,2) * b(2,2);</div><div class="line"><a name="l00302"></a><span class="lineno">  302</span>&#160;            result(2,1) = a(1,0) * b(2,0) + a(1,1) * b(2,1) + a(1,2) * b(2,2);</div><div class="line"><a name="l00303"></a><span class="lineno">  303</span>&#160;            result(2,2) = a(2,0) * b(2,0) + a(2,1) * b(2,1) + a(2,2) * b(2,2);</div><div class="line"><a name="l00304"></a><span class="lineno">  304</span>&#160;        }</div><div class="line"><a name="l00305"></a><span class="lineno">  305</span>&#160;</div><div class="line"><a name="l00306"></a><span class="lineno">  306</span>&#160;</div><div class="line"><a name="l00307"></a><span class="lineno">  307</span>&#160;        <span class="keyword">template</span> &lt;<span class="keyword">typename</span> TReal&gt;</div><div class="line"><a name="l00308"></a><span class="lineno">  308</span>&#160;        <span class="keyword">inline</span> <span class="keywordtype">void</span> multiply(</div><div class="line"><a name="l00309"></a><span class="lineno">  309</span>&#160;            matrix&lt;TReal, 4, 4&gt;&amp; result,</div><div class="line"><a name="l00310"></a><span class="lineno">  310</span>&#160;            <span class="keyword">const</span> TReal factor</div><div class="line"><a name="l00311"></a><span class="lineno">  311</span>&#160;            )</div><div class="line"><a name="l00312"></a><span class="lineno">  312</span>&#160;        {</div><div class="line"><a name="l00313"></a><span class="lineno">  313</span>&#160;            result(0) *= factor;</div><div class="line"><a name="l00314"></a><span class="lineno">  314</span>&#160;            result(1) *= factor;</div><div class="line"><a name="l00315"></a><span class="lineno">  315</span>&#160;            result(2) *= factor;</div><div class="line"><a name="l00316"></a><span class="lineno">  316</span>&#160;            result(3) *= factor;</div><div class="line"><a name="l00317"></a><span class="lineno">  317</span>&#160;            result(4) *= factor;</div><div class="line"><a name="l00318"></a><span class="lineno">  318</span>&#160;            result(5) *= factor;</div><div class="line"><a name="l00319"></a><span class="lineno">  319</span>&#160;            result(6) *= factor;</div><div class="line"><a name="l00320"></a><span class="lineno">  320</span>&#160;            result(7) *= factor;</div><div class="line"><a name="l00321"></a><span class="lineno">  321</span>&#160;            result(8) *= factor;</div><div class="line"><a name="l00322"></a><span class="lineno">  322</span>&#160;            result(9) *= factor;</div><div class="line"><a name="l00323"></a><span class="lineno">  323</span>&#160;            result(10) *= factor;</div><div class="line"><a name="l00324"></a><span class="lineno">  324</span>&#160;            result(11) *= factor;</div><div class="line"><a name="l00325"></a><span class="lineno">  325</span>&#160;            result(12) *= factor;</div><div class="line"><a name="l00326"></a><span class="lineno">  326</span>&#160;            result(13) *= factor;</div><div class="line"><a name="l00327"></a><span class="lineno">  327</span>&#160;            result(14) *= factor;</div><div class="line"><a name="l00328"></a><span class="lineno">  328</span>&#160;            result(15) *= factor;</div><div class="line"><a name="l00329"></a><span class="lineno">  329</span>&#160;        }</div><div class="line"><a name="l00330"></a><span class="lineno">  330</span>&#160;</div><div class="line"><a name="l00331"></a><span class="lineno">  331</span>&#160;        <span class="keyword">template</span> &lt;<span class="keyword">typename</span> TReal&gt;</div><div class="line"><a name="l00332"></a><span class="lineno">  332</span>&#160;        <span class="keyword">inline</span> <span class="keywordtype">void</span> multiply(</div><div class="line"><a name="l00333"></a><span class="lineno">  333</span>&#160;            matrix&lt;TReal, 2, 2&gt;&amp; result,</div><div class="line"><a name="l00334"></a><span class="lineno">  334</span>&#160;            <span class="keyword">const</span> TReal factor</div><div class="line"><a name="l00335"></a><span class="lineno">  335</span>&#160;            )</div><div class="line"><a name="l00336"></a><span class="lineno">  336</span>&#160;        {</div><div class="line"><a name="l00337"></a><span class="lineno">  337</span>&#160;            result(0) *= factor;</div><div class="line"><a name="l00338"></a><span class="lineno">  338</span>&#160;            result(1) *= factor;</div><div class="line"><a name="l00339"></a><span class="lineno">  339</span>&#160;            result(2) *= factor;</div><div class="line"><a name="l00340"></a><span class="lineno">  340</span>&#160;            result(3) *= factor;</div><div class="line"><a name="l00341"></a><span class="lineno">  341</span>&#160;        }</div><div class="line"><a name="l00342"></a><span class="lineno">  342</span>&#160;</div><div class="line"><a name="l00343"></a><span class="lineno">  343</span>&#160;</div><div class="line"><a name="l00344"></a><span class="lineno">  344</span>&#160;        <span class="keyword">template</span> &lt;<span class="keyword">typename</span> TReal&gt;</div><div class="line"><a name="l00345"></a><span class="lineno">  345</span>&#160;        <span class="keyword">inline</span> TReal dot(<span class="keyword">const</span> vector&lt;TReal, 4&gt;&amp; a, <span class="keyword">const</span> vector&lt;TReal, 4&gt;&amp; b)</div><div class="line"><a name="l00346"></a><span class="lineno">  346</span>&#160;        {</div><div class="line"><a name="l00347"></a><span class="lineno">  347</span>&#160;            <span class="keywordflow">return</span> a(0)*b(0) + a(1)*b(1) + a(2)*b(2) + a(3)*b(3);</div><div class="line"><a name="l00348"></a><span class="lineno">  348</span>&#160;        }</div><div class="line"><a name="l00349"></a><span class="lineno">  349</span>&#160;</div><div class="line"><a name="l00350"></a><span class="lineno">  350</span>&#160;</div><div class="line"><a name="l00351"></a><span class="lineno">  351</span>&#160;    }; <span class="comment">// End of namespace detail.</span></div><div class="line"><a name="l00352"></a><span class="lineno">  352</span>&#160;</div><div class="line"><a name="l00353"></a><span class="lineno">  353</span>&#160;</div><div class="line"><a name="l00354"></a><span class="lineno">  354</span>&#160;}; <span class="comment">// End of namespace polar.</span></div><div class="line"><a name="l00355"></a><span class="lineno">  355</span>&#160;</div><div class="line"><a name="l00356"></a><span class="lineno">  356</span>&#160;</div><div class="line"><a name="l00357"></a><span class="lineno">  357</span>&#160;</div><div class="line"><a name="l00358"></a><span class="lineno">  358</span>&#160;</div><div class="line"><a name="l00359"></a><span class="lineno">  359</span>&#160;<span class="preprocessor">#endif // __POLAR_DECOMPOSITION_3X3_MATRIX_H__</span></div><div class="ttc" id="structpolar_1_1detail_1_1math__utils_html"><div class="ttname"><a href="structpolar_1_1detail_1_1math__utils.html">polar::detail::math_utils</a></div><div class="ttdef"><b>Definition:</b> polar_decomposition_3x3_matrix.h:43</div></div>
<div class="ttc" id="classpolar_1_1detail_1_1matrix_html"><div class="ttname"><a href="classpolar_1_1detail_1_1matrix.html">polar::detail::matrix</a></div><div class="ttdef"><b>Definition:</b> polar_decomposition_3x3_matrix.h:145</div></div>
<div class="ttc" id="namespacepolar_html"><div class="ttname"><a href="namespacepolar.html">polar</a></div><div class="ttdef"><b>Definition:</b> polar_decomposition_3x3.h:32</div></div>
<div class="ttc" id="classpolar_1_1detail_1_1vector_html"><div class="ttname"><a href="classpolar_1_1detail_1_1vector.html">polar::detail::vector</a></div><div class="ttdef"><b>Definition:</b> polar_decomposition_3x3_matrix.h:200</div></div>
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